BUG: Fix polar angle in MinMaxCurvatureFlowFunction threshold

[physwkim]

The 3-D min/max threshold rescaled the gradient to length StencilRadius and then passed a component of it to acos(), which needs a unit-length cosine. Addresses B7 of #6575.

Root cause

MinMaxCurvatureFlowFunction::ComputeThreshold(const Dispatch<3> &, ...) (itkMinMaxCurvatureFlowFunction.hxx:311):

gradMagnitude = std::sqrt(gradMagnitude) / static_cast<PixelType>(m_StencilRadius);
...
theta = std::acos(gradient[2]);   // :326

After that division each gradient[k] is r * cos(theta_k), not cos(theta_k). The clamp to [-1, 1] just below hides the domain violation, so no NaN appears — the function silently returns the wrong polar angle. With the default StencilRadius of 2, a true cos(theta) = 0.4 (theta = 66.4 deg) is evaluated as acos(0.8) = 36.9 deg, which puts the stencil's perpendicular sample points on the wrong ring and selects the wrong min/max curvature update.

Normalizing to unit length is the fix: the downstream position reconstruction already multiplies by m_StencilRadius explicitly. The 2-D dispatch (:246) shares the rescale but reaches atan2 on a ratio, where the length cancels — no defect there, left alone.

Local validation

New GoogleTest itkMinMaxCurvatureFlowFunctionGTest.cxx, registered in a new ITKCurvatureFlowGTests driver.

• MinMaxCurvatureFlowFunction.ComputeUpdateUsesCorrectPolarAngleAtRadiusTwo — fail-before: result = 1 (the buggy angle selects the wrong branch). Pass-after: result = 0. Both values were derived from the test field's geometry before running.
• ctest -R CurvatureFlow: itkMinMaxCurvatureFlowImageFilterTest, itkBinaryMinMaxCurvatureFlowImageFilterTest, itkCurvatureFlowTesti all pass before and after. They are 100-iteration convergence checks with tolerances, so they do not pin the per-step angle.

AI assistance

• Tool: Claude Code
• Role: implementation and regression-test authoring from the B7 analysis in BUG: Findings collected while porting ~60 filters — reported together in one issue #6575
• All code was reviewed, built, and tested locally before committing

Historical context for the removed division and the measured downstream impact (SimpleITK baselines) are documented in #6619.

[greptile-apps]

Greptile Summary

This PR fixes the 3D min/max curvature threshold angle calculation. The main changes are:

• Unit-normalizes the 3D gradient before computing the polar angle.
• Keeps the existing stencil-radius scaling in the 3D sample reconstruction.
• Adds a focused GoogleTest regression for the radius-two update path.
• Registers the new CurvatureFlow GoogleTest driver.

Confidence Score: 5/5

This looks safe to merge.

No blocking issues found in the changed code.

T-Rex Logs

What T-Rex did

• The build command completed successfully with exit code 0, and Ninja reported no work to do, indicating a clean reusable build tree.
• The focused CTest run completed successfully with exit code 0 and reported 100% tests passed (3 tests in total).
• Artifacts documenting the build and test run, including commands, directories, timestamps, and verbose outputs, were captured for review.

_{Ran code and verified through T-Rex}

Important Files Changed

Filename	Overview
Modules/Filtering/CurvatureFlow/include/itkMinMaxCurvatureFlowFunction.hxx	Normalizes the 3D threshold gradient to unit length before spherical angle calculation.
Modules/Filtering/CurvatureFlow/test/CMakeLists.txt	Adds the new CurvatureFlow GoogleTest source list and driver registration.
Modules/Filtering/CurvatureFlow/test/itkMinMaxCurvatureFlowFunctionGTest.cxx	Adds a direct regression test for the corrected radius-two 3D update decision.

_{Reviews (1): Last reviewed commit: "BUG: Fix polar angle in MinMaxCurvatureF..." | Re-trigger Greptile}